Hide It or Unbundle It: A Comparison of the Antitrust Investigations Against Microsoft in the U.S. and the E.U.

[Excerpt] Microsoft Corporation, the world’s largest software company, has been facing antitrust scrutiny globally. In the U.S., after what’s been called the antitrust trial of the century, a consent decree was reached between Microsoft, the United States government, and several states, that closely resembled the litigated remedy that the remaining states received. Only Massachusetts appealed the litigated remedy, which was approved by the appeals court on June 30, 2004. In the United States, Microsoft was required to hide, but not remove, the Internet Explorer browser on the Windows Operating System. While antitrust litigation was ongoing in the United States against Microsoft, the European Union (“E.U.”) was also investigating Microsoft under E.U. antitrust law. In March, 2004, after a five year investigation, the European Union Commission fined Microsoft 497 million euros, required Microsoft to offer the Windows operating system without Windows Media Player, and required Microsoft to disclose interfaces to competitors. On December 22, 2004, the E.U.’s Court of First Instance denied Microsoft’s request for a stay of this order, and ordered Microsoft to comply; the full appeal is pending at the time of this publication. This article will examine, compare, and contrast the protracted antitrust litigation that Microsoft has faced in the U.S. and the E.U. This article will then examine what further antitrust problems Microsoft may be facing

Geometric Analysis of Synchronization in Neuronal Networks with Global Inhibition and Coupling Delays

We study synaptically coupled neuronal networks to identify the role of coupling delays in network's synchronized behaviors. We consider a network of excitable, relaxation oscillator neurons where two distinct populations, one excitatory and one inhibitory, are coupled and interact with each other. The excitatory population is uncoupled, while the inhibitory population is tightly coupled. A geometric singular perturbation analysis yields existence and stability conditions for synchronization states under different firing patterns between the two populations, along with formulas for the periods of such synchronous solutions. Our results demonstrate that the presence of coupling delays in the network promotes synchronization. Numerical simulations are conducted to supplement and validate analytical results. We show the results carry over to a model for spindle sleep rhythms in thalamocortical networks, one of the biological systems which motivated our study. The analysis helps to explain how coupling delays in either excitatory or inhibitory synapses contribute to producing synchronized rhythms.Comment: 43 pages, 12 figure

Phase models and clustering in networks of oscillators with delayed coupling

We consider a general model for a network of oscillators with time delayed, circulant coupling. We use the theory of weakly coupled oscillators to reduce the system of delay differential equations to a phase model where the time delay enters as a phase shift. We use the phase model to study the existence and stability of cluster solutions. Cluster solutions are phase locked solutions where the oscillators separate into groups. Oscillators within a group are synchronized while those in different groups are phase-locked. We give model independent existence and stability results for symmetric cluster solutions. We show that the presence of the time delay can lead to the coexistence of multiple stable clustering solutions. We apply our analytical results to a network of Morris Lecar neurons and compare these results with numerical continuation and simulation studies